The idea: The Spectres were saving the galaxy long before Shepard joined their ranks. The main character is one of the first agents invited to the organization, founded right before the Krogan Rebellions. He or she must perform secret missions on behalf of the Council to maintain order throughout civilized space.
Why it would work: The Spectres are practically the Jedi of Mass Effect. It's hard not to center Mass Effect 4 around them. They have the skills and resources to save entire planets or species. Spectres also have much more freedom than members of conventional militaries so they're able to do the sort of galactic wandering that Mass Effect games are all about.
Though Shepard belonged to their ranks, we really don't know that much about the Spectres. There are said to be dozens of active Spectres so there are plenty we haven't met yet. What's more, they existed for centuries before the trilogy began so there are plenty of historical conflicts that BioWare could use for the cloak-and-dagger story.
Why it wouldn't work: Shepard was the first human Spectre so a game about the earlier Spectres would force players to become an alien, probably a salarian or asari. I'm not sure that BioWare would make a Mass Effect that didn't have a human hero - or that takes place in a time period where humans aren't part of the galactic community yet. Salarians and asari just aren't as relatable as humans and they don't offer the same level of visual customization. I mean, c'mon, they don't even have facial hair.
The other problem with a game set mere centuries before the first Mass Effect is that there's no big bad to worry about. The krogan are fierce warriors but they seem mundane after three games, especially compared to the Reapers. The only foe that could measure up to the Reapers would probably be something BioWare invented just for this game. That would create a big story problem because if something as big as the Reapers came through just before the trilogy, everyone should still be talking about it during those games.